Question
Suppose that the reliability of a COVID test is
specified as follows: Of people having COVID, 90% of the test detect the disease but 10% go undetected. Of people free of COVID, 99% of the test are judged COVID–ive but 1% are diagnosed as showing COVID+ive. From a large population of which only 0.1% have COVID, one person is selected at random, given the COVID test, and the pathologist reports him/her as COVID+ive. What is the probability that the person actually has COVID?Solution
Let E denote the event that the person selected is actually having COVID and A the event that the person's COVID test is diagnosed as +ive. We need to find P(E|A). Also, E’ denotes the event that the person selected is actually not having COVID. Clearly, {E, E'} is a partition of the sample space of all people in the population. We are given that P(E) = 0.1% = 0.1/100 = 0.001 P(E') = 1 – P(E) = 0.999 P(A|E) = P(Person tested as COVID+ive given that he/she is actually having COVID) = 90% = 90/100 = 0.9 and P(A|E') = P(Person tested as COVID +ive given that he/she is actually not having COVID) = 1% = 1/100 = 0.01 Now, by Bayes' theorem P(E|A) = [P(E) × P(A|E)]/[P(E) × P(A|E) + P(E') × P(A|E')] = [0.001 × 0.9]/[0.001 × 0.9 + 0.999 × 0.01] = 90/1089 = 0.083 approx.
In the questions given below, a part of the sentence is given in bold. Below each sentence, some phrases are given which can substitute the bold part ...
For several decades, successful governments in Karnataka have attempted to make it necessitates for students to learn Kannada as a subject.
...A mistake that firms and valuation experts seem to make is that they overestimate the Indian economy’s availability to consume services as they ac...
of global freshwater resources (A)/ 20% of greenhouse gas emissions (B)/and is responsible for over (C)/ agriculture consumes nearly 70% (D)Â
A market-driven approaching for provide  district hospital beds for only those with the means would defeat the objective.
Which of the phrases a, b, c, and d given below in each sentence should replace the word/phrase printed in bold in the sentence to make it grammaticall...
One bright day, a thief break to a rich merchant’s house.
Direction: In the sentence given below, a part is highlighted and suggestions for its correction are given below the sentence. Choose the correct opti...
Is this the same book like our teacher recommended?
Of the four given options, choose the most appropriate one.
Relevant for Exams:
